Systems with network structures characterizing their functioning are veins in tumours [1]}, channels transporting nutrients in leaves [2]}, [3]}, animals' vasculature [4]}, microorganisms with adaptive vein networks as the Physarum polycephalum [5]}, [6]}, and Dictyostelium discoideum [7]}, transportation systems [8]}, or electrical networks [9]}. Formal systems as the travelling salesman problem [10]}, the Steiner tree geometries [11]}, and the first passage percolation [12]} are challenging network optimisation problems in graphs, with important applications in physics, biology and engineering.
